IEEE C802.16m-08/749
Project
IEEE 802.16 Broadband Wireless Access Working Group <http://ieee802.org/16>
Title
Modulation for LDPC Codes
Date
Submitted
2008-07-07
Source(s)
Rongdao Yu, Martin Liu, Chongli Liu
Voice: 86-755-28970182
E-mail: [email protected]
Huawei
Re:
IEEE 802.16m-08/024 - Call for Contributions on Project 802.16m System Description
Document (SDD), for “Hybrid ARQ” topic.
Abstract
This document proposes a kind of modulation scheme for LDPC Codes.
Purpose
For discussion and approval by TGm.
Notice
Release
Patent
Policy
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Further information is located at <http://standards.ieee.org/board/pat/pat-material.html> and
<http://standards.ieee.org/board/pat>.
Modulation for LDPC Codes
Rongdao Yu ,Martin Liu, Chongli Liu
Huawei
Introduction
LDPC code is a good code with perfect performance and thought to be a candidate code in WiMax. However,
there still remain several problems which prevent the code from standardization, e. g. implementation of
HARQ, MIMO and modulation. In this contribution, we have proposed solutions for these problems and also
with some evaluation based the theoretical analyzed tools.
Modulation for LDPC Codes
As a block code, a LDPC code can be illustrated by its parity check matrix or bipartite graph equivalently. The
degree distribution (λ, ρ), which indicates the fraction of edges with different degrees, is the most important
parameter for the performance [1, 2, 3]. The variable nodes with large degrees have more contribution to the
system performance. Following is a parity check matrix of a LDPC and its degree distribution.
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IEEE C802.16m-08/749
1
1
H 
0

0
0 1 0 1 0 1 0
1 0 1 1 1 1 1
1 0 0 0 1 1 0

1 0 1 1 0 1 1
deg 2 3 1 2 3 2 4 2
In high order modulation scheme, e. g. 16 QAM or 64 QAM, bits in a symbol may have different transmission
power. In Figure 1, we’d like to take 16 QAM as an example to illustrate the new scheme. In Figure 1, we could
find that b1 and b3 have larger power than b0 and b2 do.
Figure 1 Constellation of 16 QAM
Description of the scheme
stream 1
data
LDPC
coder
MUX
Modulation
stream 2
Figure 2 Structures for the Scheme
In order to illustrate the scheme, here we use the structure as in Figure 2.The data firstly are coded by LDPC
encoder and then fed into the multiplexer (MUX in Figure2). In the MUX entity, the bits are mapped into 2
streams by their degrees where the important bits with large degrees are in stream 1 and the rest are in stream 2.
Then the 2 streams are modulated by the Modulation entity.
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IEEE C802.16m-08/749
L1
L1
S1
L2
L2
L3
S2
L3
L4
S3
S1
Stream 1
S2
L4
S4
S3
S4
Stream 2
Figure 3 Bits of LDPC code mapped into 2 streams by degree in MUX
(L means large degree, S means small degree)
Figure 3 shows the mapping process in MUX entity, however, it is only an example and the actually mapping
relationship is determined by the encoder and probably is different with Figure 3. In the figure, bits with large
degrees which are green ones are mapped into Stream 1, and bits with small degrees which are yellow ones
would be mapped into Stream 2. Hence the important bits with large degrees are transmitted in Stream 1 and the
rest are in Stream 2.
In Figure 1, we could find that b1 and b3 have larger power than b0 and b2 do. Since the bits with larger degrees
have more contribution to the decoding process, they would be prior to be mapped onto b1 and b3 while the rest
bits with smaller degrees onto b0 and b2.
Simulation
Simulation parameter
Bandwidth
FFT size
CP Ratio
Modulation
Code Type
Code Rate
Channel
value
10M
1024
1/8
16QAM
LDPC
1/2
ITU6
3
IEEE C802.16m-08/749
0
10
normal scheme
proposed scheme
-1
BER
10
-2
10
-3
10
6
7
8
9
10
SNR(dB)
11
12
13
14
From the simulation result, we can conclude that the proposed scheme can get 0.5dB gain over than the normal
scheme at BER@1e-2, 1dB gain at BER @1e-1.
Conclusion
In this contribution, the different contribution of bits with different degrees has been investigated and the
modulation for LDPC Codes has been presented in this contribution. The simulation of the new modulation
scheme is done and the result also shows the new scheme outperform the random mapping.
References
[1]. Y Cao, Jian Gu, Lin Qi, Dacheng Yang , Degree Distribution Based HARQ for Irregular LDPC, Electronics
Letters Vol. 42, Issue 6, March 2006, pp 363-364
[2]. S. Y. Chung, T. J. Richardson, and R. L. Urbanke, Analysis of sum-product decoding of low-density paritycheck codes using a Gaussian approximation, IEEE Trans. Inform. Theory, vol. IT 47, Feb. 2001, pp. 657670.
[3]. T. J. Richardson, A. Shokrollahi, and R. L. Urbanke, Design of capacity approaching irregular low density
parity check codes, IEEE Trans. Inform. Theory, vol. 47, Feb. 2001, pp.619 - 637.
Text Proposal to SDD
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IEEE C802.16m-08/749
------------------------------------Start text proposal-----------------------------------[Adopt the following text in the ToC of P802.16m System Description Document (SDD)]
11. x.x.x Link Adaptation
For modulation of LDPC code , bits with large degree should be mapped to the bits with high reliability in
constellation of 16QAM and 64QAM.
------------------------------------End text proposal------------------------------------
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